Wind-induced turbulent entrainment across a stable density interface

1973 ◽  
Vol 61 (2) ◽  
pp. 275-287 ◽  
Author(s):  
Jin Wu
Keyword(s):  
Friction Velocity ◽  
Mixing Layer ◽  
Rate Of Change ◽  
Entrainment Rate ◽  
Homogeneous Fluid ◽  
Density Interface ◽  
Seasonal Thermocline ◽  
Turbulent Entrainment ◽  
Fluid Layers ◽  
Work Done

Turbulent entrainment across a density interface is studied in a laboratory wind–wave tank in which a stably stratified system consisting of two homogeneous fluid layers is introduced. The results indicate that the rate of change of the potential energy of the mixing layer is proportional to the rate of work done by the wind. However, only a very small fraction of the work done by the wind is used for interfacial mixing or developing a seasonal thermocline. A formula relating the entrainment rate to the density stratification and the wind-friction velocity is derived from the experimental results.

On turbulent entrainment at a stable density interface

1977 ◽  
Vol 79 (04) ◽  
pp. 753 ◽  
Author(s):  
L. H. Kantha ◽  
O. M. Phillips ◽  
R. S. Azad
Keyword(s):  
Density Interface ◽  
Turbulent Entrainment

Mechanical power and work of cat soleus, gastrocnemius and plantaris muscles during locomotion: possible functional significance of muscle design and force patterns.

1996 ◽  
Vol 199 (4) ◽  
pp. 801-814 ◽  
Author(s):  
B I Prilutsky ◽  
W Herzog ◽  
T L Allinger
Keyword(s):  
Electrical Activity ◽  
Mechanical Energy ◽  
Fibre Length ◽  
Rate Of Change ◽  
The Body ◽  
Mechanical Power ◽  
Step Cycle ◽  
Extensor Muscles ◽  
Work Done ◽  
Positive Work

Electrical activity, forces, power and work of the soleus (SO), the gastrocnemius (GA) and the plantaris (PL) muscles were measured during locomotion in the cat in order to study the functional role of these ankle extensor muscles. Forces and electrical activity (EMG) of the three muscles were measured using home-made force transducers and bipolar, indwelling wire electrodes, respectively, for walking and trotting at speeds of 0.4 to 1.8 m s-1 on a motor-driven treadmill. Video records and a geometrical model of the cat hindlimb were used for calculating the rates of change in lengths of the SO, GA and PL muscles. The instantaneous maximum possible force that can be produced by a muscle at a given fibre length and the rate of change in fibre length (termed contractile abilities) were estimated for each muscle throughout the step cycle. Fibre lengths of the SO, GA and PL were calculated using a planar, geometrical muscle model, measured muscle forces and kinematics, and morphological measurements from the animal after it had been killed. Mechanical power and work of SO, GA and PL were calculated for 144 step cycles. The contribution of the positive work done by the ankle extensor muscles of one hindlimb to the increase of the total mechanical energy of the body (estimated from values in the literature) increased from 4-11% at speeds of locomotion of 0.4 and 0.8 m s-1 to 7-16% at speeds of 1.2 m s-1 and above. The relative contributions of the negative and positive work to the total negative and positive work done by the three ankle extensor muscles increased for GA, decreased for SO and remained about the same for PL, with increasing speeds of locomotion. At speeds of 0.4-0.8 m s-1, the positive work normalized to muscle mass was 7.5-11.0 J kg-1, 1.9-3.0 J kg-1 and 5.3-8.4 J kg-1 for SO, GA and PL, respectively. At speeds of 1.2-1.8 m s-1, the corresponding values were 9.8-16.7 J kg-1, 6.0-10.7 J kg-1 and 13.4-25.0 J kg-1. Peak forces of GA and PL increased and peak forces of SO did not change substantially with increasing speeds of locomotion. The time of decrease of force and the time of decrease of power after peak values had been achieved were much shorter for SO than the corresponding times for GA and PL at fast speeds of locomotion. The faster decrease in the force and power of SO compared with GA and PL was caused by the fast decrease of the contractile abilities and the activation of SO. The results of this study suggest that the ankle extensor muscles play a significant role in the generation of mechanical energy for locomotion.

Confined turbulent entrainment across density interfaces

2015 ◽  
Vol 779 ◽  
pp. 116-143 ◽  
Author(s):  
Ajay B. Shrinivas ◽  
Gary R. Hunt
Keyword(s):  
Secondary Flow ◽  
Power Law ◽  
Lower Layer ◽  
Experimental Studies ◽  
Density Interface ◽  
Turbulent Entrainment ◽  
Steady Rate ◽  
Density Interfaces ◽  
Universal Law ◽  
Physical Reasons

In pursuit of a universal law for the rate of entrainment across a density interface driven by the impingement of a localised turbulent flow, the role of the confinement, wherein the environment is within the confines of a box, has to date been overlooked. Seeking to unravel the effects of confinement, we develop a phenomenological model describing the quasi-steady rate at which buoyant fluid is turbulently entrained across a density interface separating two uniform layers within the confines of a box. The upper layer is maintained by a turbulent plume, and the localised impingement of a turbulent fountain with the interface drives entrainment of fluid from the upper layer into the lower layer. The plume and fountain rise from sources at the base of the box and are non-interacting. Guided by previous observations, our model characterises the dynamics of fountain–interface interaction and the steady secondary flow in the environment that is induced by the perpetual cycle of vertical excursions of the interface. We reveal that the dimensionless entrainment flux across the interface $E_{i}$ is governed not only by an interfacial Froude number $\mathit{Fr}_{i}$ but also by a ‘confinement’ parameter ${\it\lambda}_{i}$, which characterises the length scale of interfacial turbulence relative to the depth of the upper layer. By deducing the range of ${\it\lambda}_{i}$ that may be regarded as ‘small’ and ‘large’, we shed new light on the effects of confinement on interfacial entrainment. We establish that for small ${\it\lambda}_{i}$, a weak secondary flow has little influence on $E_{i}$, which follows a quadratic power law $E_{i}\propto \mathit{Fr}_{i}^{2}$. For large ${\it\lambda}_{i}$, a strong secondary flow significantly influences $E_{i}$, which then follows a cubic power law $E_{i}\propto \mathit{Fr}_{i}^{3}$. Drawing on these results, and showing that for previous experimental studies ${\it\lambda}_{i}$ exhibits wide variation, we highlight underlying physical reasons for the significant scatter in the existing measurements of the rate of interfacial entrainment. Finally, we explore the implications of our results for guiding appropriate choices of box geometry for experimentally and numerically examining interfacial entrainment.

scholarly journals A relook at radiation by a point charge. I

2017 ◽  
Vol 95 (11) ◽  
pp. 1142-1149
Author(s):  
Nitin Ramchandra Gadre
Keyword(s):  
Point Charge ◽  
Poynting Vector ◽  
Classical Model ◽  
Delta Function ◽  
Rate Of Change ◽  
Surface Integral ◽  
Surface Integration ◽  
Energy And Momentum ◽  
Work Done ◽  
The Relationship

Efforts to suggest a classical model for the hydrogen atom are discouraged by a conclusion, based on the principles of electrodynamics, that an accelerating charged particle necessarily radiates. In this paper, we re-examine the steps leading to this conclusion. We start with the relativistic expressions for energy and momentum of a particle and establish the relationship between special relativity and electrodynamics. The standard field expression and its relativistic transformations are then studied for a point charge source, represented by a delta function. In conventional Poynting’s theorem analysis, the rate of change of work done on a system of charges is written as addition of two terms, rate of change of stored energy, and surface integral of Poynting vector. For a delta function source, the first two terms of this equation are either non-integrable or difficult to evaluate. Only the third surface integration term can be evaluated, which is said to give radiation by the point charge. Thus, the statement that an accelerated charge radiates is a conclusion based on this Poynting vector analysis. We examine it and realize that this statement, namely, that a point charge radiates continuously just because it is accelerating, does not have adequate theoretical justification.

On the energy deficiency in self-preserving convective flows

1972 ◽  
Vol 53 (2) ◽  
pp. 217-226 ◽  
Author(s):  
J. S. Turner
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Transition Zone ◽  
Similarity Solutions ◽  
Turbulent Convection ◽  
Energy Deficiency ◽  
Convective Flows ◽  
Density Interface ◽  
Buoyancy Forces ◽  
Work Done

When similarity solutions are used to describe convective plumes or thermals, there is always found to be a discrepancy between the work done by buoyancy forces and the kinetic energy of mean motion. It is the main purpose of this paper to set down the ratio of these quantities for a wide variety of forms of buoyant elements and environmental stabilities. For consistency, the remaining fraction of the energy must appear as turbulent kinetic energy and eventually be dissipated, but these processes are not investigated in detail. The results are shown to have some relevance to the problem of convectively driven mixing across a density interface, where the largest scales of motion are dominant, and to the understanding of the transition zone between two self-preserving states of turbulent convection.

scholarly journals Effects of mean shear on the local turbulent entrainment process

2013 ◽  
Vol 731 ◽  
pp. 95-116 ◽  
Author(s):  
Marc Wolf ◽  
M. Holzner ◽  
B. Lüthi ◽  
D. Krug ◽  
W. Kinzelbach ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Rate Of Change ◽  
Surface Shape ◽  
Small Scale ◽  
Geometrical Shape ◽  
Viscous Effects ◽  
Interface Position ◽  
Entrainment Velocity ◽  
Turbulent Entrainment ◽  
Entrainment Process

AbstractWe report on effects of mean shear on the turbulent entrainment process, focusing in particular on their relation to small-scale processes in the proximity of the turbulent/non-turbulent interface (TNTI). Three-dimensional particle tracking velocimetry (3D-PTV) measurements of an axisymmetric jet are compared to data from a direct numerical simulation (DNS) of a zero-mean-shear (ZMS) flow. First, conditional statistics relative to the interface position are investigated in a pseudo-Eulerian view (i.e. in a fixed frame relative to the interface position) and in a Lagrangian view. We find that in a pseudo-Eulerian frame of reference, both vorticity fluctuations and mean shear contribute to the vorticity jump at the boundary between irrotational and turbulent regions. In contrast, the Lagrangian evolution of enstrophy along trajectories crossing the entrainment interface is almost exclusively dominated by vorticity fluctuations, at least during the first Kolmogorov time scales after passing the interface. A mapping between distance to the instantaneous interface versus conditional time along the trajectory shows that entraining particles remain initially close to the TNTI and therefore attain lower average enstrophy values. The ratio between the rate of change of enstrophy in the two frames of references defines the local entrainment velocity ${v}_{n} = - (\mathrm{D} {\omega }^{2} / \mathrm{D} t)/ (\partial {\omega }^{2} / \partial {\hat {x} }_{n} )$, where ${\omega }^{2} $ is enstrophy and ${\hat {x} }_{n} $ is the coordinate normal to the TNTI. The quantity ${v}_{n} $ is decomposed into mean and fluctuating components and it is found that mean shear enhances the local entrainment velocity via inviscid and viscous effects. Further, the analysis substantiates that for all investigated flow configurations the local entrainment velocity depends considerably on the geometrical shape of the interface. Depending on the surface shape, different small-scale mechanisms are dominant for the local entrainment process, i.e. viscous effects for convex shapes and vortex stretching for concave shapes, looking from the turbulent region towards the convoluted boundary. Moreover, turbulent fluctuations display a stronger dependence on the shape of the interface than mean shear effects.

scholarly journals The First 3D Simulations of Carbon Burning in a Massive Star

2016 ◽  
Vol 12 (S329) ◽  
pp. 237-241 ◽  
Author(s):  
A. Cristini ◽  
C. Meakin ◽  
R. Hirschi ◽  
D. Arnett ◽  
C. Georgy ◽  
...  
Keyword(s):  
Stellar Evolution ◽  
Radial Profile ◽  
Three Dimensional ◽  
Stable Region ◽  
Entrainment Rate ◽  
Convective Boundary ◽  
Boundary Mixing ◽  
Turbulent Entrainment ◽  
Large Eddy ◽  
Carbon Burning

AbstractWe present the first detailed three-dimensional hydrodynamic implicit large eddy simulations of turbulent convection for carbon burning. The simulations start with an initial radial profile mapped from a carbon burning shell within a 15 M⊙stellar evolution model. We considered 4 resolutions from 1283to 10243zones. These simulations confirm that convective boundary mixing (CBM) occurs via turbulent entrainment as in the case of oxygen burning. The expansion of the boundary into the surrounding stable region and the entrainment rate are smaller at the bottom boundary because it is stiffer than the upper boundary. The results of this and similar studies call for improved CBM prescriptions in 1D stellar evolution models.

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